Hamilton-Jacobi Tunneling Method for Dynamical Horizons in Different Coordinate Gauges

TL;DR

This paper develops a Hamilton-Jacobi tunneling approach for dynamical horizons, emphasizing invariant quantities and coordinate choices, and applies it to black holes and cosmological models to clarify temperature and emission rate issues.

Contribution

It introduces a coordinate-invariant Hamilton-Jacobi tunneling method for dynamical horizons and applies it to black hole and cosmological models, clarifying temperature and emission rate ambiguities.

Findings

Clarifies the role of coordinate systems in horizon tunneling.

Demonstrates positivity of temperature in FRW models.

Resolves ambiguities related to temperature doubling in static cases.

Abstract

Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunneling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two natural requirements, namely that the tunneling rate is an observable and therefore it must be based on invariantly defined quantities, and that coordinate systems which do not cover the horizon should not be admitted. These simple observations can help to clarify some ambiguities, like the doubling of the temperature occurring in the static case when using singular coordinates, and the role, if any, of the temporal contribution of the action to the emission rate. The formalism is also applied to FRW cosmological models, where it is observed that it predicts the positivity of the temperature naturally, without further assumptions on the sign of the energy.